Okay so I've noticed that when they have an immunity challenge someone gives the Idol back to Jeff.
That Idol that they give back is the hidden one found on exile Island right?
In a word, no.
The idol in the immunity challenges is the one for the team; it is not designated for an individual. It is given out at each immunity challenge and stays that way until the challenges become individual. At that point, it generally changes to some sort of necklace that the individual wears at tribal council to designate their immunity.
When someone finds the hidden immunity idol, it is their choice as to whether they let people know they have it. Generally it is a strategic move to only let people in your alliance know you possess the idol. When played correctly, it will completely flip a vote determined to go one way. For example, in Micronesia, Amanda played the hidden immunity idol so any of the votes that were cast for her did not count. If she hadn't played the idol, she would have been voted out 4-2. Instead, none of the votes counted and Alexis was voted out by a 2-0 vote. The idol has to be played AFTER voting at tribal council. In previous seasons, they were able to play the idol after the votes had been read; it has now been amended to where the person has to play the idol before the votes are read. In Cook Islands, Yul flat out let people know he had the idol. It can be played in a number of ways...but for more of a blindside effect, people generally don't let on that they have it.
The clue at Exile Island stated that the idol was hidden back at their camp...therefore making it a [I]hidden[/I] immunity idol. Brendan found the idol at his camp...it will be interesting to see if he lets anyone know that he has it. He can also give it to someone to save them, so if his 4some alliance works out, he could give it to Sierra, Taj, or Stephen (assuming he's the 4th) to save them. Sugar did that with Matty in Gabon.